Molecular, Cellular & Tissue Biomechanics Patrick Doyle (ChemE), Roger Kamm (ME & BE) Maxine Jonas (BE) Goal: Develop a fundamental understanding of biomechanics over a wide range of length scales. MOLECULAR MECHANICS I Biomolecules and intermolecular forces II Single molecule biopolymer mechanics III Formation and dissolution of bonds IV Motion at the molecular/macromolecular level TISSUE MECHANICS I Molecular structure --> physical properties II Continuum, elastic models (stress, strain, constitutive laws) III Viscoelasticity IV Poroelasticity V Electrochemical effects on tissue properties CELLULAR MECHANICS I Structure/function/properties of the cell II Biomembranes III The cytoskeleton IV Cell adhesion and aggregation V Cell migration VI Mechanotransduction Typical Length Scales in Biology microtubule typical DNA width width length of DNA in a animal cell chromosome human -9 -7 -5 -3 -1 1 10 10 10 10 10 10 meters histone chromatin nucleus proteins width length of DNA contained in a typical human cell Similar spectra exist in time scales or energy scales. molecular motor semiflexible polymer Muscles: Spanning from Macro to Nano Actin: semiflexible polymer Myosin: molecular motor Titin: resting elasticity Macro-scale applications Cardiovascular mechanics 108 bpm 72 bpm Computational fluid mechanics used to study shear stresses in the carotid artery Image removed due to Image removed due to copyright considerations. copyright considerations. Peak flow Maximum Image removed due to Image removed due to copyright considerations. copyright considerations. deceleration …or tissue stresses in the wall of a diseased vessel Image removed due to copyright considerations. Stress (Pa) Computational mesh for finite element analysis Image removed due to copyright considerations. Image removed due to copyright considerations. Histological section obtained from surgery MRI images Vessel cross-sections Boundary data (x,y,z) IGES boundary : Quilting / Knitting Finite element mesh 3D model ParaSolid Model Modeling Complex Material Properties� Continuum Microstructural� bending plate entangled polymer Constitutive relations and force balance Viscoelastic or poroelastic strut model solid t21(t) † Typical Eukaryotic Cell� 10-30 mm 1 mm = 10-6 m� 1 nm = 10-9 m� 1 Å = 10-10m� Plasma Membrane� Plasma Membrane 2-D Elastic Plate ~5 nm Cytoskeleton� Cytoskeletal TEM cytoskeleton photograph, J. Hartwig, Harvard University. fibers Courtesy of J. Hartwig. Used with permission. “rigidity” Diameter (nm) Persistence Length (mm) actin 6-8 15 microtubule 10 60,000� intermediate 20-25 1-3 filament When stressed, cells form stress fibers, mediated by a variety of actin-binding proteins. TEM cytoskeleton photograph, J. Hartwig, Harvard University. Courtesy of John Hartwig. Used with permission. Structure of actin.� Image courtesy of Dr. Willy Wriggers. Used with permission. � Measuring Complex Material Properties� Aspiration Cell Poking� Thermal tracers� 4 2 0 -2 -4 -6 -6 -4 -2 0 2 4 Cell Adhesion� Physical forces effect bond association/dissociation Finite contact times Cell deformation After Orsello, Lauffenburger and Hammer, 2001. Dynamic Processes: Cell Migration Cell Motility Fluorescently marked actin • Actin is a polymer • The cytoskeleton is active • Coordinated processes: adhesion, (de-) polymerization Active Cell Contraction Cardiac myocyte (Jan Lammerding) Courtesy of Jan Lammerding, Harvard Medical School. Used with permission. Cytoskeletal Mechanics Probed by External Force Image removed due to copyright considerations. Fibroblast with fluorescent mitochondria forced by a magnetic bead D. Ingber, P. LeDuc Mechanotransduction: Hair cell stimulation tip link tension in tip link increases stereocilium Image removed due to Tension in the tip copyright considerations. link activates a stretch-activated SEM of the Image removed due to stereocilia on the copyright considerations. ion channel, leading surface of a single to intracellular calcium ion hair cell (Hudspeth) fluctuations. Molecular dynamics simulation of channel regulation by membrane tension Images removed due to copyright considerations. See Figures 1 and 9 in Gullingsrud, Justin, Dorina Kosztin, and Klaus Schulten. "Structural Determinants of MscL Gating Studied by Molecular Dynamics Simulations." Biophys J, Vol. 80, No. 5 (May 2001), p. 2074-2081. http://www.biophysj.org/cgi/content/full/80/5/2074 But other evidence suggests that the pore increases to >20 angstroms! Steered molecular dynamics of fibronectin Constant applied force = Images removed due to copyright considerations. 500 pN See Figures 2 and 3 in Gao, Mu, David Craig, Viola Vogel, and Klaus Schulten. "Identifying unfolding intermediates of FN-III10 by steered molecular dynamics." Unfolding has Journal of Molecular Biology, 323:939-950 (2002). been thought to be important in exposing buried cryptic binding sites. The Orders of Magnitude in DNA Organization Image removed due to copyright considerations. Diagram showing range of size magnitudes, from metaphase chromosome (1400 nm) down to short region of DNA double-helix (2 nm). Compaction of a stretched DNA after histones are introduced. Image removed due to copyright considerations. See Figure 1 in Ladoux, B., P. Doyle et al. "Fast kinetics of chromatin assembly revealed by single-molecule videomicroscopy and scanning force microscopy." Proc Natl Acad Sci U S A. 97(26):14251-6 (2000 Dec 19). Dynamic Processes: Molecules Single T4-phage Stretching a Single DNA DNA in solution Image removed due to copyright considerations. 1996 Group Bustmante Doyle • Thermal forces are important (kT/ 1 nm ~ 4 x 10 -12 N ) • Entropic & enthalpic effects • Generic/specific mechanical responses • Single molecule experiments are possible Motor Proteins Mechanochemical (Enzyme) Engines ATP hydrolysis->conformation change Rotary Motor (F0F1) Linear Motor Myosin II 1999 Image removed due to Image removed due to copyright considerations. copyright considerations. Yanagida Yanagida Actin filament Motor Proteins Reoccurring Themes in Biomechanics • Multiple length/time/energy scales • Polymers play an important role • Thermal energy is important • Interplay of chemical, electrical, mechanical interactions • Quantitative (single molecule) experiments Molecular, Cellular & Tissue Biomechanics Biology is soft, wet & dynamic Using Engineering/Physics to Unravel & Manipulate Biology • Scaling arguments • Mechanical models (polymer physics) • Experimental techniques • Importance of the stochastic nature of biology Readings There is no single text which covers all of this material ! Texts: Y. C. Fung, Biomechanics: Mechanical Properties of Living Tissues, 2nd Edition, Springer -Verlag, 1993R. Nossal and L. Lecar, Molecular and Cellular Biophysics, Wiley, 1990.H. Lodish, D. Baltimore, L. Zipurksy, P. Matsudaira, Molecular Cell Biology, 1996. K. Dill and S. Bromberg, Molecular Driving Forces, 2003 Manuscript Drafts: P.C. Nelson, Biological Physics: Energy, Information Life A. Grodzinksy, R. Kamm, L. Mahadevan: BEH 410 Research Articles: Posted/linked on the web Notes: Periodically posted.